Find a unit vector w in the direction of u?

Let vec uu=<<4/343,-1,2/323>>

1 Answer
Jul 24, 2018

(4/sqrt29,-3/sqrt29,2/sqrt29).(429,329,229).

Explanation:

vecww and vecuu have the same direction.

:. vecw=kvecu=k(4/3,-1,2/3)," where, "k gt 0,

, or, vecw=(4/3k,-k,2/3k).

Also, vecw is requred to be a unit vector.

:. ||vecw||=1.

:. sqrt{(4/3k)^2+(-k)^2+(2/3k)^2}=1.

:. sqrt(29/9k^2)=1.

:. sqrt29/3|k|=1.

:. k=+3/sqrt29, because, k gt 0.

rArrvecw=(4/sqrt29,-3/sqrt29,2/sqrt29), is the desired vector.